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Grading Sheet~~~~~~~~~~~~~~

MIME 3470—Thermal Science Laboratory~~~~~~~~~~~~~~Experiment №. 5

VISCOSITY

Students’ Names / Section №

POINTS SCORE TOTALAPPEARANCE, ORGANIZATION, ENGLISH, & GRAMMAR (Applicable

to both MS Word and Mathcad sections) 5

ORDERED DATA, CALCULATIONS & RESULTS—MATHCAD

FALLING SPHERE VISCOMETER

VARIABLE DEFINITIONS AND RAW DATA 5 CALCULATIONS (INCLUDING REYNOLDS NUMBER) WITH DETAILED EXPLANATIONS 10

VISCOSITY VALUES 5SAYBOLT VISCOMETER

VARIABLE DEFINITIONS AND RAW DATA 5 CALCULATIONS WITH DETAILED EXPLANATIONS 5 VISCOSITY VALUES 5STORMER VISCOMETER

VARIABLE DEFINITIONS AND RAW DATA 5 CALCULATIONS WITH DETAILED EXPLANATIONS 10 CALIBRATION CHART FOR 2 MASSES 5 VISCOSITY VALUES 5TECHNICAL WRITTEN CONTENT

TABLE OF 3 VISCOSITY PAIRS (W/IN RED BOX OVER MATHCAD) 5 DISCUSSION OF RESULTS

WHY FILL SAYBOLT CONTAINER TO OVERFLOWING …? 5HOW WOULD ONE INTERPOLATE TABLE 1 DATA? 5WHY MUST THE GLYCERIN & OIL BE AT THE SAME TEMPS? 5WHICH METHOD IS BEST? WHY? 5

CONCLUSIONS 5ORIGINAL DATASHEET 5

TOTAL 100

COMMENTS

GRADER—d

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MIME 3470—Thermal Science Laboratory~~~~~~~~~~~~~~Experiment №. 5

VISCOSITY~~~~~~~~~~~~~~

LAB PARTNERS: NAME NAME

NAME NAME

NAME NAME

SECTION №EXPERIMENT TIME/DATE: TIME, DATE

~~~~~~~~~~~~~~OBJECTIVE—This experiment is performed to familiarize the future engineer with three of the many methods of measuring viscosity. In particular, a falling sphere viscometer, a Saybolt viscometer, and a Stormer viscometer will be used to measure viscosity of the same fluid (a motor oil) at room temperature.

INTRODUCTION—One of the properties of homogeneous fluids is its resistance to motion. A measure of this resistance is known as viscosity1. The engineer has to have knowledge of viscosity for a wide range of applications. For example, it is very important to select a fluid of proper viscosity for use in a hydraulic machine. Furthermore, vis-cosity enters into the calculation of pressure losses through pipes, the determination of pump sizes, the calculation of fluid forces, etc. Thus, it is helpful for the engineer to have a physical awareness of viscosity and a background in how viscosity is measured. A viscosity measure-ment is generally made with a device known as a viscometer. There are several methods of determining viscosity, three of which will be demonstrated in this experiment. These methods are 1) Falling sphere method, 2) Saybolt viscometer, and 3) Stormer viscometer.

It is worth noting that viscosity is a measure of relative fluidity at some definite temperature. Since viscosity varies considerably with tem-perature, it is essential that the fluid be at a constant and uniform tem-perature when a measurement is being made. The scope of this expe-riment will not include the varying effect of temperature on viscosity.

Viscosity can be reported as dynamic viscosity, m, or kinematic viscosity, n = m/rf, where rf, is the density of the fluid. In SI measure, dynamic viscosity is reported in units of centipoises where 1 cP = 1 m×Pa×s while kinematic viscosity is reported in units of centistokes where 1 cSt = 1´ 10–6 m2/s. 1. FALLING SPHERE VISCOMETER —This type of viscosity measurement is based on Stokes’ law and terminal velocity. Stokes’ law is applicable for extremely low Reynolds number flow; i.e., creeping or drifting flow (Re < 1).

Procedure—Fill the graduated cylinder with motor oil of unknown viscosity all the way to the top graduation. Drop a sphere into the oil and record the time it takes the sphere to travel a given distance within the cylinder. The distance can be easily laid out by applying tape at two locations along the cylinder. Remember that it takes the sphere a few moments to reach terminal velocity; thus, the upper tape demarcation should not be at the level of the free surface. Using a stop watch, the constant (terminal) velocity between the tape-marked locations is determined. Using the calculated velocity, the Reynolds number can be obtained. The inside diameter. Dcyl, of the graduated cylinder should also be measured.

In order to obtain spheres of a density that is slightly greater than the density of the fluid, plastic spheres are used. To determine the density of the sphere material, measure the diameter of ten spheres. Then, use the average of each of these measurements and the measured mass of all ten spheres to compute a density of the sphere material. Also measure a mass of a known volume of the fluid using a balance and a graduated flask. This can be done using the 60cc flask for the Saybolt viscometer, weighing it empty and full.

Calculations and Results —A blank Mathcad object has been supplied for the viscosity calculations of this experiment in the section entitled ORDERED DATA, CALCULATIONS AND RESULTS. There, the student should compute a Reynolds number based on the terminal velocity to verify that, indeed, Re < 1. In cases where Re > 1, charts of drag coefficients versus Reynolds number for spheres can be found in any fluids textbook. The Reynolds number is defined as

(1)

where, rf density of the fluid Vterm terminal velocity of sphere in the fluid

D diameter of the spherem unknown viscosity of the fluid.

The unknown viscosity is determined from Stokes’ law using the measured terminal velocity calculated as

(2)

where, g acceleration of gravityr density of the sphere.

Report both dynamic and kinematic viscosities in the space provided in the Mathcad object.

Note that Stokes’ law only applies to spheres and it assumes an infinite fluid around the sphere. The presence of the cylinder walls will cause a higher fluid velocity around the sphere. If D/Dcyl > 1/3, this wall effect

can be approximately accounted for by using

(3)

where, V true fluid velocity as experienced by the sphereDtube inside diameter of the graduated cylinder or tube.

2. UNIVERSAL SAYBOLT VISCOMETER —The Saybolt method requires the measurement of time for a certain volume of fluid to flow through a capillary or a tube of very small diameter. The Saybolt viscometer consists of four containers of constant volume capacity with capillary outlet tubes at the bottom. The containers are immersed in an oil bath for which the temperature can be closely controlled (this experiment will be carried out at room temperature). A container must be filled all the way up to the edge (with a bit of overflow) with the oil of unknown viscosity. Excess oil must be removed from the annulus. A pipette is recommended for the removal . Explain in the discussion why filling the oil to overflowing is important and why the annulus needs to be cleaned. Once the excess oil has been removed, oil is allowed to flow through the capillary tube into the constant volume flask (60 ml) placed below it. Simultaneously, the time it takes the oil to fill the flask is recorded. The time recorded can be converted into units of viscosity by making use of the provided chart (see Figure 2).

Fi

gure 1—Saybolt viscometer

1 viscosity: < Latin, viscosus, sticky (also viscum, bird lime, a sticky subs-tance made from mistletoe berries that is spread on twigs to capture birds)

OVERFLOW ANNULUSTHERMOMETER

FILL TO HERE

RESERVOIR

CORKLIQUID BATH

CONTAINER

OIL

HEATING UNIT

60 CC

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Procedure—Three of the four tubes have Universal orifices and one tube has a Furol2

orifice. The oil, whose viscosity is to be determined, is placed in one of the containers having a Universal orifice. The container must be filled to the edge. The temperature of the unknown oil may be controlled by means of an oil bath surrounding the cylinder. However, in all three parts of this experiment the fluid will be tested at room temperature. With the fluid at room temperature, the oil in the cylinder is allowed to flow through the capillary tube into the 60cc container below. As soon as the oil begins to flow, the stopwatch is started. Timing stops when the oil in the container below reaches a specified volume of 60cc. The elapsed time is known as Saybolt Universal Seconds, SUS, or Saybolt Furol Seconds, SFS, depending on which orifice is used. The Saybolt seconds can be converted to SI viscosity units of centistokes or English Gravitational units of ft2/s by means of the following formulae:

SI , 32s £

SUS £ 100s

, SUS

100sEnglish Gravitational

, 32s £

(4)

The metric equations graph as shown below.

Figure 2— Kinematic Viscosity, cSt, vs. Saybolt Universal Seconds, SUS

Calculations and Results : Convert SUS reading into centistokes and centipoises and report in the box provided over the Mathcad object.

3. STORMER VISCOMETER —is a rotational viscometer. It consists of two concentric cylinders that are rotated with respect to one another. The narrow annular space between the cylinders is filled with liquid whose viscosity is to be measured. As the width of the annular space is small compared with the diameter of the annulus, the sheared flow produced is almost identical to the flow that would be produced by two flat plates—Newton’s intended experiment. For a known annular distance and relative angular velocity of the outer and inner surfaces of the annulus, Newton’s law of viscosity can be used to determine the absolute (dynamic) viscosity.

Newton’s law of viscosity is

where, t – uniform shearing stress over width of annulusm – absolute viscosity

Vx – velocity in direction of shearing, for the annulus, this is the tangential velocity

y – direction normal to the shearing (radial direction)dVx/dy – velocity gradient due to shearing—in this case, it is

constant (linear profile)

The rotational speed under an applied constant torque is inversely proportional to the fluid viscosity. The principal difficulty with this type of viscometer is that mechanical friction must be accounted for, and this is difficult to determine accurately.

Figure 3—Stormer Viscometer

Detailed Procedure —Make sure that the cylinder that holds the test fluid is absolutely clean. Using glycerine3

as a calibrating fluid, measure the time (seconds) for 20 revolutions using two different masses on the hanger. This will produce two different shearing rates and driving shearing stresses. Then, clean and dry the cylinder that holds the liquid and load the sample of the fluid of unknown viscosity. Test the sample using the same procedure.

Dynamic Viscosity of 100% Glycerine (Centipoises)Temperature (°C )

0 10 20 30 40 50 60 70 80 90 10012070 3900 1410 612 284 142 81.3 50.6 31.9 21.3 14.8

Table 1-Temperature dependence of glycerin’s dynamic viscosity http://www.dow.com/glycerine/resources/table18.htm,

In plotting the data listed in Table 1, one must observe the highly non-linear viscosity-temperature dependence. This makes the evaluation of viscosity at room temperature (»20ºC) difficult. Fortunately, UT’s Bruce Poling (Professor, ChEE) in Reference [A]4

has supplied the following equation for the absolute viscosity of glycerol:

, (applicable range 273 £ T £ 303ºK)The curve fitted data shown in Figure 4 indicates a good agreement between experimental data of Table 1 and predictions made with the above equation. Density data downloaded from the same URL is shown in Table2 and is also plotted in Figure 4. As one might expect, density is linear enough to interpolate.

2 furol: a contraction of “fuel and road oils” 3 glycerin, glycerine: [<Gr. glykeros, sweet] nontechnical term for glycerol. glycerol: [glycer(in) + -OL {Þ an alcohol or phenol}] an odorless,

colorless, syrupy liquid, C3H

5(OH)

3, prepared by the hydrolysis of fats and oils: it is used as a solvent, skin lotion, food preservative, etc.

4 References [B] and [C] may have similar data.

0 20 40 60 80 100 120 140 160 180 2000

5

10

15

20

25

30

35

40

45

50

trace 1trace 2

Saybolt Universal Seconds, SUS

Kin

em

atic

Vis

cosi

ty,

cSt

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In the discussion, explain how one would interpolate the data of Table 1 if the Poling equation just above were not available.

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Density of 100% Glycerine, (g/cm3)Temperature (°C)

15 15.5 20 25 30

1.26415 1.26381 1.26108 1.25802 1.25495 Table 2 – Glycerin density variation with temperature

http://www.dow.com/glycerine/resources/table4_91100.htm

Figure 4—Fit of experimental data for the dynamic viscosity and of

glycerol. Density data is also plotted.

Calculations and Results—Calculate absolute viscosity following the outlined procedure (which indirectly makes use of Newton’s law of viscosity). Construct a calibration chart (Viscosity vs. Time for 20 Revolutions) for the Stormer viscometer for each of the driving weights. Complete the chart by joining each of the datum points to the origin. Use markers (both vertical and horizontal) in Mathcad to denote the intersection on each line of time and computed viscosity. Since this is not a traditional graphical solution, one has to calculate it and then plot it.

Now the viscosity of the unknown oil can be determined using the constructed calibration chart. Use the same two driving weights as before to determine two values for the unknown viscosity, then calculate the average value of the two to be reported. One must take extra care to insure that the temperature of the oil is the same as the temperature of the calibrating glycerol since the calibrating chart can only be used under these conditions. Explain why this is so in the discussion. Report both dynamic and kinematic viscosity in the summary box of the Mathcad calculations.

Finally, in the discussion, explain which of the three methods is best? Why?

References[A] Reid, Robert C., Prausnitz, John M., Poling, Bruce E., The

Properties of Gases and Liquids, McGraw-Hill Book Company, 4th edition, 1987.

[B] Yaws, Carl L., Handbook of Viscosity, Gulf Publishing Company, 1995

[C] Daubert, Thomas E. and Danner, R.P., Physical and Thermodynamic Properties of Pure Chemicals: Data Compilation, 5 Volumes, Taylor & Francis, 1996

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ORDERED DATA, CALCULATIONS, AND RESULTS THE RED BOX BELOW RESIDES OVER THE MATHCAD OBJECT & CAN BE RESIZED A/O MOVED.

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DISCUSSION OF RESULTS

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In the Saybolt part of the lab, explain why filling the oil to over-flowing is important and why the annulus needs to be cleaned?

Answer here

.

How one would interpolate the data of Table 1 if the Poling equation were not available?

Answer here

One must take extra care to insure that the temperature of the oil is the same as the temperature of the calibrating glycerol since the calibrating chart can only be used under these conditions. Explain why this is so.

Answer here

Explain which of the three methods is best? Why? Answer here

CONCLUSIONS

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APPENDICES

APPENDIX A —DATA SHEET FOR VISCOSITY EXPERIMENT

Time/Date: _______________________

Lab Partners: _______________________ _______________________ _______________________

_______________________ _______________________ _______________________

1. Falling Sphere Viscometer

To Compute Density of Sphere MaterialFor 10

Spheres,Sphere O.D.,

cm.

Average O.D. cm

10 Spheres Total Mass, g

To Compute Density of Fluid For 1 Sphere, Measure Terminal Velocity Drift Time

Fluid Motor Oil

Fluid Temperature, ºC . Sphere Diameter, cm .Mass of Empty Saybolt 60cc Flask, g . Fall Distance, cm .Mass of Flask with Fluid Sample, g . Fall Time, s .Fluid Sample Size, ml

Use Saybolt 60 cc flask

I.D. of Cylinder .

2. Saybolt Viscometer

Fluid Motor Oil Fluid Temperature, ºC Same as aboveSaybolt Universal Seconds for 60cc Sample, s .

3. Stormer Viscometer

Glycerin Calibration Runs

Run Temperature, ºC Hung Mass, g Time for 20 revs, s

1 Same as above

2 Same as above

Motor Oil Runs

1 Same as above

2 Same as above

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